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4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and number of particles N, may be written as N! N(E,N) = E N!N2! - .. with the restrictions EN; = N and DGN; = E. Except for an additive constant, show that the entropy per par- ticle is given by

4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and number of particles N, may be written as N! N(E,N) = E N!N2! - .. with the restrictions EN; = N and DGN; = E. Except for an additive constant, show that the entropy per par- ticle is given by

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and number of particles N, may be written as N! Ω (Ε, N) = Σ N!N2! ... N1.N2. with the restrictions EN; = N and EGN; = E. Except for an additive constant, show that the entropy per par- ticle is given by s = -kB In where {Ñ;} is the set of occupation numbers at equilibrium. Using the continuum limit of the Boltzmann gas, show that the entropy depends on temperature according to a term of the form kg In T (note the correction!).
Transcribed Image Text:4. The total number of the accessible microscopic states of the Boltzmann gas, with energy E and number of particles N, may be written as N! Ω (Ε, N) = Σ N!N2! ... N1.N2. with the restrictions EN; = N and EGN; = E. Except for an additive constant, show that the entropy per par- ticle is given by s = -kB In where {Ñ;} is the set of occupation numbers at equilibrium. Using the continuum limit of the Boltzmann gas, show that the entropy depends on temperature according to a term of the form kg In T (note the correction!).
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